This letter proposes performance evaluation of phase-only correlation (POC) functions using signal-to-noise ratio (SNR) and peak-to-correlation energy (PCE). We derive the general expressions of SNR and PCE of the POC functions as correlation performance measures. SNR is expressed by simple fractional function of circular variance. PCE is simply given by squared peak value of the POC functions, and its expectation can be expressed in terms of circular variance.

In the field of adaptive notch filtering, Monotonically Increasing Gradient (MIG) algorithm has recently been proposed by Sugiura and Shimamura [1], where it is claimed that the MIG algorithm shows monotonically increasing gradient characteristics. However, our analysis has found that the underlying theory in [1] includes crucial errors. This letter shows that the formulation of the gradient characteristics in [1] is incorrect, and reveals that the MIG algorithm fails to realize monotonically increasing gradient characteristics when the input signal includes white noise.

In this paper, we use a modified Gaussian filter to improve enlargement accuracy of the arbitrary scale LP enlargement method, which is based on the Laplacian pyramid representation (so called "LP method"). The parameters of the proposed algorithm are extracted through a theoretical analysis and an experimental estimation. Experimental results show that the proposed modified Gaussian filter is effective for the arbitrary scale LP enlargement method.

This letter proposes a Perfect-Reconstruction (PR) encryption scheme based on a PR QMF bank. Using the proposed scheme, signals can be encrypted and reconstructed perfectly by using two Periodically Time-Varying (PTV) digital filters respectively. Also we find that the proposed scheme has a "good" encryption effect and compares favorably with frequency scramble in the aspects of computation complexity, PR property, and degree of security.

This paper proposes a statistical expression of the output error variance due to coefficient quantization in separable denominator M-D digital filters. Using this expression, this paper shows that minimization of overall quantization errors can be performed by minimizing the roundoff noise.

This paper proposes statistical analysis of phase-only correlation functions with phase-spectrum differences following wrapped distributions. We first assume phase-spectrum differences between two signals to be random variables following a linear distribution. Next, based on directional statistics, we convert the linear distribution into a wrapped distribution by wrapping the linear distribution around the circumference of the unit circle. Finally, we derive general expressions of the expectation and variance of the POC functions with phase-spectrum differences following wrapped distributions. We obtain exactly the same expressions between a linear distribution and its corresponding wrapped distribution.

In this paper, we propose an enlargement method for images with Gaussian noise based on the Laplacian pyramid (LP) representation. Unlike lowpass pre-processing approaches to the LP enlargement method, an embedded approach is used in this paper. Since the amplitude of Gaussian noise signals is smaller than the amplitude of image edge signals in the predicted LP stage, we adopt a modified ε-filter in the proposed LP enlargement algorithm to reduce the Gaussian noise. Experimental results show that the proposed method can obtain high accuracy denoise enlarged images.

The aim of this study is to improve the accuracy of flicker parameters estimation in old film sequences in which moving objects are present. Conventional methods tend to fail in flicker parameters estimation due to the effects of moving objects. Our proposed method firstly utilizes an adaptive Gaussian mixture model (GMM)-based method to detect the moving objects in the film sequences, and combines the detected results with the histogram-matched frames to generate reference frames for flicker parameters estimation. Then, on the basis of a linear flicker model, the proposed method uses an M-estimator with the reference frames to estimate the flicker parameters. Experimental results show that the proposed method can effectively improve the accuracy of flicker parameters estimation when the moving objects are present in the film sequences.

In this paper, we propose a novel bicubic method for digital image interpolation. Since the conventional bicubic method does not consider image local features, the interpolated images obtained by the conventional bicubic method often have a blurring problem. In this paper, the proposed bicubic method adopts both the local asymmetry features and the local gradient features of an image in the interpolation processing. Experimental results show that the proposed method can obtain high accuracy interpolated images.

On the basis of the controllability gramians, the observability gramians and the second order modes, this paper shows that optimal realizations (filter structures having minimum roundoff noises) of quarter-plane-causal, recursive and separable in denominator 2-D digital filters (CRSD filters for short) are scaled and rotated balanced realizations. Two applications of this relation are given. The first one gives a simple proof of the absence of overflow oscillations in optimal realizations. The second one, which is the main result of this paper, gives a direct design method of CRSD filters in the spatial domain. This method simplifies traditional two-step design (approximation and synthesis) into a one-step design with much less computational complexity. Resulting filters of this direct design method can approximate given 2-D impulse responses closely. In addition, they are always guaranteed to be stable, nearly optimal with respect to roundoff noise and free of overflow oscillations. The efficiency of the direct design method is shown by numerical examples.

This paper studies the design problem of causal, recursive and separable denominator (CRSD) 3-D state-space digital filters. First, a balanced approximation method and a synthesis method of optimal realizations of CRSD 3-D digital filters are proposed by introducing the concept of characteristic filters. Then, a simple equivalent relation between balanced realizations and optimal realizations of CRSD 3-D digital filters is revealed. Using this relation and the balanced approximation method proposed, this paper proposes a spatial-domain direct design method of CRSD 3-D digital filters. This direct design method can perform approximation and synthesis of CRSD 3-D digital filters simultaneously. Further, it can result in stable state-space digital filters which are nealy optimal with respect to roundoff noise, and free of overflow oscillations. Effciency of direct design method is shown by a numerical example.

The average coefficient sensitivity is defined for 2-D systems described by Roesser's local state space model. The sensitivity can be computed by using the 2-D observability Gramian and the 2-D controllability Gramian, which are also called the 2-D noise matrix and the 2-D covariance matrix if the 2-D systems are considered to be 2-D digital filters. Minimization of sensitivity via 2-D equivalent transforms is studied in cases of having no constraint and having a scaling constraint on the state vector. In the first case, the minimum sensitivity realizations are equivalent to the 2-D balanced realizations modulo a block orthogonal transform. In the second case, the 2-D systems are considered to be 2-D digital filters and the minimization of sensitivity is equivalent to the minimization of roundoff noise under l2-norm scaling constraint. An example is given to show method of analysing and minimizing the sensitivity of 2-D systems.

This paper designs and evaluates highly parallel VLSI processors for real time 2-D state-space digital filters using hierarchical behavioral description language and synthesizer. The architecture of the 2-D state-space digital filtering system is a linear systolic array of homogeneous VLSI processors, each of which consists of eight processing elements (PEs) executing 1-D state-space digital filtering with multi-input and multi-output. Hierarchical behavioral description language and synthesizer are adopted to design and evaluate PE's and the VLSI processors. One 16 bit fixed-point PE executing a (4, 4)-th order 2-D state-space digital filtering is described on the basis of distributed arithmetic in about 1,200 steps by the description language and is composed of 15 K gates in terms of 2 input NAND gate. One VLSI processor which is a cascade connection of eight PEs is composed of 129 K gates and can be integrated into one 1515 [mm2] VLSI chip using 1 µm CMOS standard cell. The 2-D state-space digital filtering system composed of 128 VLSI processors at 25 MHz clock can execute a 1,0241,024 image in 1.47 [msec] and thus can be applied to real-time conventional video signal processing.

This paper proposes a closed form solution to L2-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the second-order case of state-space digital filters, we can express the L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, the L2-sensitivity minimization problem can be converted into a problem to find the solution to a fourth-degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations.

This paper proposes closed form solutions to the L2-sensitivity minimization subject to L2-scaling constraints for second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. We can express the L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, L2-sensitivity is expressed in closed form, and its minimization subject to L2-scaling constraints is achieved without iterative calculations.

This paper studies the model reduction of separable denominator multi-dimensional (SD M-D, M is used as an integer) linear, shift-invariant systems (systems for short). First, it shows that the controllability, observability and stability of an SD M-D system are completely determined by M 1-D multi-input multi-output systems, which are referred to as the characteristic systems in this paper. Then the balanced realizations of SD M-D systems are defined, and a synthesis method of such realizations is given. Finally, a model reduction method based on the balanced realizations is proposed. Validity of this method is illustrated by a numerical example of a 3-D system.

In order to suppress constant input limit cycles in 2-D separable denominator digital filters, bias cancel realizations are proposed by modifying 2-D separable denominator digital filters free of zero imput limit cycles.

This paper proposes the statistical analysis of phase-only correlation functions between two real signals with phase-spectrum differences. For real signals, their phase-spectrum differences have odd-symmetry with respect to frequency indices. We assume phase-spectrum differences between two signals to be random variables. We next derive the expectation and variance of the POC functions considering the odd-symmetry of the phase-spectrum differences. As a result, the expectation and variance of the POC functions can be expressed by characteristic functions or trigonometric moments of the phase-spectrum differences. Furthermore, it is shown that the peak value of the POC function monotonically decreases and the sidelobe values monotonically increase as the variance of the phase-spectrum differences increases.

A new approach to design variable IIR digital filters by using a cascade of N identical individual filters of any order n is proposed in this paper. First, the approximation method for lowpass filter specifications is outlined, then the general limitations of the new method are investigated and a compact formula is derived. Next, the limitations for the main canonic approximations (Butterworth, Chebyshev and Elliptic) are investigated and compared and convenient expressions for design and evaluation are obtained. New first- and second-order filter sections, permitting very easy tuning of the cutoff frequency by recalculating and reprogramming of a single multiplier coefficient value, are developed and the design and tuning strategies for highpass, bandpass and bandstop filters are proposed. Finally design examples are given and the sound superiority of the new method compared to other known is demonstrated experimentally.